/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
D(b(x:S,y:S)) -> b(D(x:S),D(y:S))
D(c(x:S,y:S)) -> b(c(y:S,D(x:S)),c(x:S,D(y:S)))
D(constant) -> h
D(div(x:S,y:S)) -> m(div(D(x:S),y:S),div(c(x:S,D(y:S)),pow(y:S,2)))
D(ln(x:S)) -> div(D(x:S),x:S)
D(m(x:S,y:S)) -> m(D(x:S),D(y:S))
D(opp(x:S)) -> opp(D(x:S))
D(pow(x:S,y:S)) -> b(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
D(t) -> s(h)
b(b(x:S,y:S),z:S) -> b(x:S,b(y:S,z:S))
b(h,x:S) -> x:S
b(s(x:S),s(y:S)) -> s(s(b(x:S,y:S)))
b(x:S,h) -> x:S
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 D#(b(x:S,y:S)) -> D#(x:S)
 D#(b(x:S,y:S)) -> D#(y:S)
 D#(b(x:S,y:S)) -> B(D(x:S),D(y:S))
 D#(c(x:S,y:S)) -> D#(x:S)
 D#(c(x:S,y:S)) -> D#(y:S)
 D#(c(x:S,y:S)) -> B(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D#(div(x:S,y:S)) -> D#(x:S)
 D#(div(x:S,y:S)) -> D#(y:S)
 D#(ln(x:S)) -> D#(x:S)
 D#(m(x:S,y:S)) -> D#(x:S)
 D#(m(x:S,y:S)) -> D#(y:S)
 D#(opp(x:S)) -> D#(x:S)
 D#(pow(x:S,y:S)) -> D#(x:S)
 D#(pow(x:S,y:S)) -> D#(y:S)
 D#(pow(x:S,y:S)) -> B(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 B(b(x:S,y:S),z:S) -> B(x:S,b(y:S,z:S))
 B(b(x:S,y:S),z:S) -> B(y:S,z:S)
 B(s(x:S),s(y:S)) -> B(x:S,y:S)
-> Rules:
 D(b(x:S,y:S)) -> b(D(x:S),D(y:S))
 D(c(x:S,y:S)) -> b(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D(constant) -> h
 D(div(x:S,y:S)) -> m(div(D(x:S),y:S),div(c(x:S,D(y:S)),pow(y:S,2)))
 D(ln(x:S)) -> div(D(x:S),x:S)
 D(m(x:S,y:S)) -> m(D(x:S),D(y:S))
 D(opp(x:S)) -> opp(D(x:S))
 D(pow(x:S,y:S)) -> b(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 D(t) -> s(h)
 b(b(x:S,y:S),z:S) -> b(x:S,b(y:S,z:S))
 b(h,x:S) -> x:S
 b(s(x:S),s(y:S)) -> s(s(b(x:S,y:S)))
 b(x:S,h) -> x:S

Problem 1: 

SCC Processor:
-> Pairs:
 D#(b(x:S,y:S)) -> D#(x:S)
 D#(b(x:S,y:S)) -> D#(y:S)
 D#(b(x:S,y:S)) -> B(D(x:S),D(y:S))
 D#(c(x:S,y:S)) -> D#(x:S)
 D#(c(x:S,y:S)) -> D#(y:S)
 D#(c(x:S,y:S)) -> B(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D#(div(x:S,y:S)) -> D#(x:S)
 D#(div(x:S,y:S)) -> D#(y:S)
 D#(ln(x:S)) -> D#(x:S)
 D#(m(x:S,y:S)) -> D#(x:S)
 D#(m(x:S,y:S)) -> D#(y:S)
 D#(opp(x:S)) -> D#(x:S)
 D#(pow(x:S,y:S)) -> D#(x:S)
 D#(pow(x:S,y:S)) -> D#(y:S)
 D#(pow(x:S,y:S)) -> B(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 B(b(x:S,y:S),z:S) -> B(x:S,b(y:S,z:S))
 B(b(x:S,y:S),z:S) -> B(y:S,z:S)
 B(s(x:S),s(y:S)) -> B(x:S,y:S)
-> Rules:
 D(b(x:S,y:S)) -> b(D(x:S),D(y:S))
 D(c(x:S,y:S)) -> b(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D(constant) -> h
 D(div(x:S,y:S)) -> m(div(D(x:S),y:S),div(c(x:S,D(y:S)),pow(y:S,2)))
 D(ln(x:S)) -> div(D(x:S),x:S)
 D(m(x:S,y:S)) -> m(D(x:S),D(y:S))
 D(opp(x:S)) -> opp(D(x:S))
 D(pow(x:S,y:S)) -> b(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 D(t) -> s(h)
 b(b(x:S,y:S),z:S) -> b(x:S,b(y:S,z:S))
 b(h,x:S) -> x:S
 b(s(x:S),s(y:S)) -> s(s(b(x:S,y:S)))
 b(x:S,h) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(b(x:S,y:S),z:S) -> B(x:S,b(y:S,z:S))
 B(b(x:S,y:S),z:S) -> B(y:S,z:S)
 B(s(x:S),s(y:S)) -> B(x:S,y:S)
->->-> Rules:
 D(b(x:S,y:S)) -> b(D(x:S),D(y:S))
 D(c(x:S,y:S)) -> b(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D(constant) -> h
 D(div(x:S,y:S)) -> m(div(D(x:S),y:S),div(c(x:S,D(y:S)),pow(y:S,2)))
 D(ln(x:S)) -> div(D(x:S),x:S)
 D(m(x:S,y:S)) -> m(D(x:S),D(y:S))
 D(opp(x:S)) -> opp(D(x:S))
 D(pow(x:S,y:S)) -> b(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 D(t) -> s(h)
 b(b(x:S,y:S),z:S) -> b(x:S,b(y:S,z:S))
 b(h,x:S) -> x:S
 b(s(x:S),s(y:S)) -> s(s(b(x:S,y:S)))
 b(x:S,h) -> x:S
->->Cycle:
->->-> Pairs:
 D#(b(x:S,y:S)) -> D#(x:S)
 D#(b(x:S,y:S)) -> D#(y:S)
 D#(c(x:S,y:S)) -> D#(x:S)
 D#(c(x:S,y:S)) -> D#(y:S)
 D#(div(x:S,y:S)) -> D#(x:S)
 D#(div(x:S,y:S)) -> D#(y:S)
 D#(ln(x:S)) -> D#(x:S)
 D#(m(x:S,y:S)) -> D#(x:S)
 D#(m(x:S,y:S)) -> D#(y:S)
 D#(opp(x:S)) -> D#(x:S)
 D#(pow(x:S,y:S)) -> D#(x:S)
 D#(pow(x:S,y:S)) -> D#(y:S)
->->-> Rules:
 D(b(x:S,y:S)) -> b(D(x:S),D(y:S))
 D(c(x:S,y:S)) -> b(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D(constant) -> h
 D(div(x:S,y:S)) -> m(div(D(x:S),y:S),div(c(x:S,D(y:S)),pow(y:S,2)))
 D(ln(x:S)) -> div(D(x:S),x:S)
 D(m(x:S,y:S)) -> m(D(x:S),D(y:S))
 D(opp(x:S)) -> opp(D(x:S))
 D(pow(x:S,y:S)) -> b(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 D(t) -> s(h)
 b(b(x:S,y:S),z:S) -> b(x:S,b(y:S,z:S))
 b(h,x:S) -> x:S
 b(s(x:S),s(y:S)) -> s(s(b(x:S,y:S)))
 b(x:S,h) -> x:S


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 B(b(x:S,y:S),z:S) -> B(x:S,b(y:S,z:S))
 B(b(x:S,y:S),z:S) -> B(y:S,z:S)
 B(s(x:S),s(y:S)) -> B(x:S,y:S)
-> Rules:
 D(b(x:S,y:S)) -> b(D(x:S),D(y:S))
 D(c(x:S,y:S)) -> b(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D(constant) -> h
 D(div(x:S,y:S)) -> m(div(D(x:S),y:S),div(c(x:S,D(y:S)),pow(y:S,2)))
 D(ln(x:S)) -> div(D(x:S),x:S)
 D(m(x:S,y:S)) -> m(D(x:S),D(y:S))
 D(opp(x:S)) -> opp(D(x:S))
 D(pow(x:S,y:S)) -> b(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 D(t) -> s(h)
 b(b(x:S,y:S),z:S) -> b(x:S,b(y:S,z:S))
 b(h,x:S) -> x:S
 b(s(x:S),s(y:S)) -> s(s(b(x:S,y:S)))
 b(x:S,h) -> x:S
->Projection:
 pi(B) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 D(b(x:S,y:S)) -> b(D(x:S),D(y:S))
 D(c(x:S,y:S)) -> b(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D(constant) -> h
 D(div(x:S,y:S)) -> m(div(D(x:S),y:S),div(c(x:S,D(y:S)),pow(y:S,2)))
 D(ln(x:S)) -> div(D(x:S),x:S)
 D(m(x:S,y:S)) -> m(D(x:S),D(y:S))
 D(opp(x:S)) -> opp(D(x:S))
 D(pow(x:S,y:S)) -> b(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 D(t) -> s(h)
 b(b(x:S,y:S),z:S) -> b(x:S,b(y:S,z:S))
 b(h,x:S) -> x:S
 b(s(x:S),s(y:S)) -> s(s(b(x:S,y:S)))
 b(x:S,h) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 D#(b(x:S,y:S)) -> D#(x:S)
 D#(b(x:S,y:S)) -> D#(y:S)
 D#(c(x:S,y:S)) -> D#(x:S)
 D#(c(x:S,y:S)) -> D#(y:S)
 D#(div(x:S,y:S)) -> D#(x:S)
 D#(div(x:S,y:S)) -> D#(y:S)
 D#(ln(x:S)) -> D#(x:S)
 D#(m(x:S,y:S)) -> D#(x:S)
 D#(m(x:S,y:S)) -> D#(y:S)
 D#(opp(x:S)) -> D#(x:S)
 D#(pow(x:S,y:S)) -> D#(x:S)
 D#(pow(x:S,y:S)) -> D#(y:S)
-> Rules:
 D(b(x:S,y:S)) -> b(D(x:S),D(y:S))
 D(c(x:S,y:S)) -> b(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D(constant) -> h
 D(div(x:S,y:S)) -> m(div(D(x:S),y:S),div(c(x:S,D(y:S)),pow(y:S,2)))
 D(ln(x:S)) -> div(D(x:S),x:S)
 D(m(x:S,y:S)) -> m(D(x:S),D(y:S))
 D(opp(x:S)) -> opp(D(x:S))
 D(pow(x:S,y:S)) -> b(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 D(t) -> s(h)
 b(b(x:S,y:S),z:S) -> b(x:S,b(y:S,z:S))
 b(h,x:S) -> x:S
 b(s(x:S),s(y:S)) -> s(s(b(x:S,y:S)))
 b(x:S,h) -> x:S
->Projection:
 pi(D#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 D(b(x:S,y:S)) -> b(D(x:S),D(y:S))
 D(c(x:S,y:S)) -> b(c(y:S,D(x:S)),c(x:S,D(y:S)))
 D(constant) -> h
 D(div(x:S,y:S)) -> m(div(D(x:S),y:S),div(c(x:S,D(y:S)),pow(y:S,2)))
 D(ln(x:S)) -> div(D(x:S),x:S)
 D(m(x:S,y:S)) -> m(D(x:S),D(y:S))
 D(opp(x:S)) -> opp(D(x:S))
 D(pow(x:S,y:S)) -> b(c(c(y:S,pow(x:S,m(y:S,1))),D(x:S)),c(c(pow(x:S,y:S),ln(x:S)),D(y:S)))
 D(t) -> s(h)
 b(b(x:S,y:S),z:S) -> b(x:S,b(y:S,z:S))
 b(h,x:S) -> x:S
 b(s(x:S),s(y:S)) -> s(s(b(x:S,y:S)))
 b(x:S,h) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.